
derivative application
Find the equation of any quadratics that passes through the origin and are tangent to both y=2x4 and y=8x49.
I have thought about this problem for most of the afternoon now and got no where. I tried drawing it to see the problem but no good. I just don't know where to start or how to approach this problem. What/how should I be thinking?
Thank you

Hi
The quadratics you are looking for passing through the origin, their generic equation is $\displaystyle f(x) = ax^2 + bx$
The tangent at a point whose abscissa is $\displaystyle x_0$ is :
$\displaystyle T_0 : y = (2ax_0+b)xax_0^2$
The quadratics are tangent to both y=2x4 and y=8x49 iff there exists $\displaystyle x_0$ and $\displaystyle x_1$ such that
$\displaystyle 2ax_0+b = 2$
$\displaystyle ax_0^2 = 4$
$\displaystyle 2ax_1+b = 8$
$\displaystyle ax_1^2 = 49$
Solve for a, b, x0 and x1.
You will find 2 quadratics.